In 2008, Nešetřil and Ossona de Mendez introduced bounded expansion as a notion of sparsity in graph classes [1]}.
Bounded expansion generalizes proper minor-closed classes which contain (among other things) the heavily-studied bounded treewidth and planar graphs.
Nešetřil and Ossona de Mendez characterized classes with bounded expansion by the existence of low-treedepth colorings [1]}, enabling the first of many algorithmic approaches to tackle problems on these broad classes.
While part of the appeal of bounded expansion is its numerous characterizations, low-treedepth colorings alone allowed Dvořák et al. to prove that FO-Model Checking is fixed-parameter tractable (FPT) in graphs from a class of bounded expansion [3]}.
Beyond the many problems expressible in first order logic, characterizations of bounded expansion have been used to give FPT algorithms for Subgraph Counting  [4]}, Steiner Tree  [5]}, and numerous others [6]}, [7]}, [8]}.
